How to fix armature distorting my mesh?
I think the distortion may appear, because the vertices of the mesh are improperly assigned to the bone. 


Select the object you want to be affected by the bone, enter Edit Mode and in Vertex Groups panel select neck group and click Remove.


Select the head group and click Assign.


The maximum weight of the mesh is assigned to the head bone, so now all the vertices will follow the bone completely (you can see the weights entering Weight Paint mode).


Now it should work fine.